Given:

Question

𝑎
∥
𝑏
a∥b and
𝑒
∥
𝑓
e∥f Given
∠a = ∠b Corresponding angles of parallel lines
∠e = ∠f Corresponding angles of parallel lines
∠a + ∠e = 180° Opposite angles of a parallelogram
∠b + ∠f = 180° Opposite angles of a parallelogram
∠a + ∠e = ∠b + ∠f Substitution
𝑎
𝑏
‾
ab
≅
𝑒
𝑓
‾
ef
​
Vertical angles are congruent
This proof demonstrates that opposite sides of the parallelogram are congruent because they share the same measure due to corresponding angles formed by parallel lines.

Answer 1

Therefore, we can conclude that in a parallelogram, opposite sides are congruent.